"The beautiful healthy baby girl left the hospital with her ecstatic parents," says the rep, who confirmed the birth to PEOPLE exclusively.

Richie, 26, said she was pregnant in July, telling Diane Sawyer on Good Morning America: "I would really want to be someone my child would look up to."

Later, Richie, who had a famously wild childhood, said the idea of parenthood had made her more mature. "When I found out that I was pregnant, there was just something inside of me that felt a responsibility to mend any issues that I've had with my parents in the past, because, listen, I've put them through a lot," she said.

As for Good Charlotte frontman Madden, 28, he told PEOPLE in November he was looking forward to being a dad. "Having a baby is the most exciting thing that's ever happened to me, and to us," he said.

And the new parents plan to teach their little one the value of generosity. In December, the couple started the Richie Madden Children's Foundation to help the less fortunate. "We want our child to be a part of the community, and to know that there's a responsibility to help the community," Madden said at the time.

The couple have yet to set a wedding date, but in September Madden said "marriage is in our future" – he just wasn't sure when. "Right now our priority is our family and is the baby," he said. "That's all we've been thinking about. We are in love and are really happy."